1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 160,810 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… miss… e380000… nhs_glo…     1 gl34fe   South West
##  2 111       2020-03-18 fema… miss… e380001… nhs_sou…     1 ne325nn  North Eas…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_air…     8 bd57jr   North Eas…
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_ash…     7 tn254ab  South East
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_bar…     9 n111np   London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    11 s752py   North Eas…
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_bas…    19 ss143hg  East of E…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_bas…     6 dn227xf  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_bat…     9 ba25rp   South West
## # … with 160,800 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##     date_report               nhs_region deaths
## 1    2020-03-01          East of England      0
## 2    2020-03-02          East of England      1
## 3    2020-03-03          East of England      0
## 4    2020-03-04          East of England      0
## 5    2020-03-05          East of England      0
## 6    2020-03-06          East of England      1
## 7    2020-03-07          East of England      0
## 8    2020-03-08          East of England      0
## 9    2020-03-09          East of England      1
## 10   2020-03-10          East of England      0
## 11   2020-03-11          East of England      0
## 12   2020-03-12          East of England      0
## 13   2020-03-13          East of England      1
## 14   2020-03-14          East of England      2
## 15   2020-03-15          East of England      2
## 16   2020-03-16          East of England      1
## 17   2020-03-17          East of England      1
## 18   2020-03-18          East of England      5
## 19   2020-03-19          East of England      4
## 20   2020-03-20          East of England      2
## 21   2020-03-21          East of England     11
## 22   2020-03-22          East of England     12
## 23   2020-03-23          East of England     11
## 24   2020-03-24          East of England     19
## 25   2020-03-25          East of England     26
## 26   2020-03-26          East of England     36
## 27   2020-03-27          East of England     38
## 28   2020-03-28          East of England     28
## 29   2020-03-29          East of England     43
## 30   2020-03-30          East of England     45
## 31   2020-03-31          East of England     70
## 32   2020-04-01          East of England     62
## 33   2020-04-02          East of England     64
## 34   2020-04-03          East of England     80
## 35   2020-04-04          East of England     71
## 36   2020-04-05          East of England     76
## 37   2020-04-06          East of England     71
## 38   2020-04-07          East of England     93
## 39   2020-04-08          East of England    111
## 40   2020-04-09          East of England     87
## 41   2020-04-10          East of England     74
## 42   2020-04-11          East of England     92
## 43   2020-04-12          East of England    101
## 44   2020-04-13          East of England     78
## 45   2020-04-14          East of England     61
## 46   2020-04-15          East of England     82
## 47   2020-04-16          East of England     74
## 48   2020-04-17          East of England     86
## 49   2020-04-18          East of England     64
## 50   2020-04-19          East of England     67
## 51   2020-04-20          East of England     67
## 52   2020-04-21          East of England     75
## 53   2020-04-22          East of England     67
## 54   2020-04-23          East of England     49
## 55   2020-04-24          East of England     66
## 56   2020-04-25          East of England     54
## 57   2020-04-26          East of England     48
## 58   2020-04-27          East of England     46
## 59   2020-04-28          East of England     58
## 60   2020-04-29          East of England     32
## 61   2020-04-30          East of England     45
## 62   2020-05-01          East of England     49
## 63   2020-05-02          East of England     29
## 64   2020-05-03          East of England     41
## 65   2020-05-04          East of England     19
## 66   2020-05-05          East of England     36
## 67   2020-05-06          East of England     31
## 68   2020-05-07          East of England     33
## 69   2020-05-08          East of England     33
## 70   2020-05-09          East of England     29
## 71   2020-05-10          East of England     22
## 72   2020-05-11          East of England     18
## 73   2020-05-12          East of England     21
## 74   2020-05-13          East of England     27
## 75   2020-05-14          East of England     26
## 76   2020-05-15          East of England     19
## 77   2020-05-16          East of England     26
## 78   2020-05-17          East of England     17
## 79   2020-05-18          East of England     25
## 80   2020-05-19          East of England     15
## 81   2020-05-20          East of England     26
## 82   2020-05-21          East of England     21
## 83   2020-05-22          East of England     13
## 84   2020-05-23          East of England     12
## 85   2020-05-24          East of England     17
## 86   2020-05-25          East of England     25
## 87   2020-05-26          East of England     14
## 88   2020-05-27          East of England     12
## 89   2020-05-28          East of England     17
## 90   2020-05-29          East of England     16
## 91   2020-05-30          East of England      9
## 92   2020-05-31          East of England      8
## 93   2020-06-01          East of England     17
## 94   2020-06-02          East of England     14
## 95   2020-06-03          East of England     10
## 96   2020-06-04          East of England      7
## 97   2020-06-05          East of England     12
## 98   2020-06-06          East of England      5
## 99   2020-06-07          East of England      9
## 100  2020-06-08          East of England      5
## 101  2020-06-09          East of England      6
## 102  2020-06-10          East of England      8
## 103  2020-06-11          East of England      0
## 104  2020-06-12          East of England      9
## 105  2020-06-13          East of England      5
## 106  2020-06-14          East of England      4
## 107  2020-06-15          East of England      7
## 108  2020-06-16          East of England      3
## 109  2020-06-17          East of England      7
## 110  2020-06-18          East of England      4
## 111  2020-06-19          East of England      7
## 112  2020-06-20          East of England      2
## 113  2020-06-21          East of England      3
## 114  2020-06-22          East of England      6
## 115  2020-06-23          East of England      4
## 116  2020-06-24          East of England      3
## 117  2020-06-25          East of England      0
## 118  2020-06-26          East of England      3
## 119  2020-06-27          East of England      0
## 120  2020-03-01                   London      0
## 121  2020-03-02                   London      0
## 122  2020-03-03                   London      0
## 123  2020-03-04                   London      0
## 124  2020-03-05                   London      0
## 125  2020-03-06                   London      1
## 126  2020-03-07                   London      0
## 127  2020-03-08                   London      0
## 128  2020-03-09                   London      1
## 129  2020-03-10                   London      0
## 130  2020-03-11                   London      6
## 131  2020-03-12                   London      6
## 132  2020-03-13                   London     10
## 133  2020-03-14                   London     14
## 134  2020-03-15                   London     10
## 135  2020-03-16                   London     15
## 136  2020-03-17                   London     23
## 137  2020-03-18                   London     27
## 138  2020-03-19                   London     25
## 139  2020-03-20                   London     44
## 140  2020-03-21                   London     49
## 141  2020-03-22                   London     54
## 142  2020-03-23                   London     63
## 143  2020-03-24                   London     87
## 144  2020-03-25                   London    113
## 145  2020-03-26                   London    129
## 146  2020-03-27                   London    130
## 147  2020-03-28                   London    122
## 148  2020-03-29                   London    146
## 149  2020-03-30                   London    149
## 150  2020-03-31                   London    181
## 151  2020-04-01                   London    202
## 152  2020-04-02                   London    191
## 153  2020-04-03                   London    196
## 154  2020-04-04                   London    230
## 155  2020-04-05                   London    195
## 156  2020-04-06                   London    197
## 157  2020-04-07                   London    220
## 158  2020-04-08                   London    238
## 159  2020-04-09                   London    206
## 160  2020-04-10                   London    170
## 161  2020-04-11                   London    178
## 162  2020-04-12                   London    158
## 163  2020-04-13                   London    166
## 164  2020-04-14                   London    144
## 165  2020-04-15                   London    142
## 166  2020-04-16                   London    139
## 167  2020-04-17                   London    100
## 168  2020-04-18                   London    101
## 169  2020-04-19                   London    103
## 170  2020-04-20                   London     95
## 171  2020-04-21                   London     94
## 172  2020-04-22                   London    109
## 173  2020-04-23                   London     77
## 174  2020-04-24                   London     71
## 175  2020-04-25                   London     58
## 176  2020-04-26                   London     53
## 177  2020-04-27                   London     51
## 178  2020-04-28                   London     43
## 179  2020-04-29                   London     44
## 180  2020-04-30                   London     40
## 181  2020-05-01                   London     41
## 182  2020-05-02                   London     41
## 183  2020-05-03                   London     36
## 184  2020-05-04                   London     30
## 185  2020-05-05                   London     25
## 186  2020-05-06                   London     37
## 187  2020-05-07                   London     37
## 188  2020-05-08                   London     30
## 189  2020-05-09                   London     23
## 190  2020-05-10                   London     26
## 191  2020-05-11                   London     18
## 192  2020-05-12                   London     18
## 193  2020-05-13                   London     16
## 194  2020-05-14                   London     20
## 195  2020-05-15                   London     18
## 196  2020-05-16                   London     14
## 197  2020-05-17                   London     15
## 198  2020-05-18                   London      9
## 199  2020-05-19                   London     14
## 200  2020-05-20                   London     19
## 201  2020-05-21                   London     12
## 202  2020-05-22                   London     10
## 203  2020-05-23                   London      6
## 204  2020-05-24                   London      7
## 205  2020-05-25                   London      9
## 206  2020-05-26                   London     12
## 207  2020-05-27                   London      7
## 208  2020-05-28                   London      8
## 209  2020-05-29                   London      7
## 210  2020-05-30                   London     12
## 211  2020-05-31                   London      6
## 212  2020-06-01                   London     10
## 213  2020-06-02                   London      7
## 214  2020-06-03                   London      6
## 215  2020-06-04                   London      8
## 216  2020-06-05                   London      4
## 217  2020-06-06                   London      0
## 218  2020-06-07                   London      4
## 219  2020-06-08                   London      5
## 220  2020-06-09                   London      4
## 221  2020-06-10                   London      7
## 222  2020-06-11                   London      5
## 223  2020-06-12                   London      3
## 224  2020-06-13                   London      3
## 225  2020-06-14                   London      2
## 226  2020-06-15                   London      1
## 227  2020-06-16                   London      2
## 228  2020-06-17                   London      1
## 229  2020-06-18                   London      2
## 230  2020-06-19                   London      3
## 231  2020-06-20                   London      3
## 232  2020-06-21                   London      4
## 233  2020-06-22                   London      2
## 234  2020-06-23                   London      0
## 235  2020-06-24                   London      3
## 236  2020-06-25                   London      2
## 237  2020-06-26                   London      1
## 238  2020-06-27                   London      0
## 239  2020-03-01                 Midlands      0
## 240  2020-03-02                 Midlands      0
## 241  2020-03-03                 Midlands      1
## 242  2020-03-04                 Midlands      0
## 243  2020-03-05                 Midlands      0
## 244  2020-03-06                 Midlands      0
## 245  2020-03-07                 Midlands      0
## 246  2020-03-08                 Midlands      3
## 247  2020-03-09                 Midlands      1
## 248  2020-03-10                 Midlands      0
## 249  2020-03-11                 Midlands      2
## 250  2020-03-12                 Midlands      6
## 251  2020-03-13                 Midlands      5
## 252  2020-03-14                 Midlands      4
## 253  2020-03-15                 Midlands      5
## 254  2020-03-16                 Midlands     11
## 255  2020-03-17                 Midlands      8
## 256  2020-03-18                 Midlands     13
## 257  2020-03-19                 Midlands      8
## 258  2020-03-20                 Midlands     28
## 259  2020-03-21                 Midlands     13
## 260  2020-03-22                 Midlands     31
## 261  2020-03-23                 Midlands     33
## 262  2020-03-24                 Midlands     41
## 263  2020-03-25                 Midlands     48
## 264  2020-03-26                 Midlands     64
## 265  2020-03-27                 Midlands     72
## 266  2020-03-28                 Midlands     89
## 267  2020-03-29                 Midlands     92
## 268  2020-03-30                 Midlands     90
## 269  2020-03-31                 Midlands    123
## 270  2020-04-01                 Midlands    140
## 271  2020-04-02                 Midlands    142
## 272  2020-04-03                 Midlands    124
## 273  2020-04-04                 Midlands    151
## 274  2020-04-05                 Midlands    164
## 275  2020-04-06                 Midlands    140
## 276  2020-04-07                 Midlands    123
## 277  2020-04-08                 Midlands    186
## 278  2020-04-09                 Midlands    139
## 279  2020-04-10                 Midlands    127
## 280  2020-04-11                 Midlands    142
## 281  2020-04-12                 Midlands    139
## 282  2020-04-13                 Midlands    120
## 283  2020-04-14                 Midlands    116
## 284  2020-04-15                 Midlands    147
## 285  2020-04-16                 Midlands    102
## 286  2020-04-17                 Midlands    118
## 287  2020-04-18                 Midlands    115
## 288  2020-04-19                 Midlands     92
## 289  2020-04-20                 Midlands    107
## 290  2020-04-21                 Midlands     86
## 291  2020-04-22                 Midlands     78
## 292  2020-04-23                 Midlands    103
## 293  2020-04-24                 Midlands     79
## 294  2020-04-25                 Midlands     72
## 295  2020-04-26                 Midlands     81
## 296  2020-04-27                 Midlands     74
## 297  2020-04-28                 Midlands     68
## 298  2020-04-29                 Midlands     53
## 299  2020-04-30                 Midlands     56
## 300  2020-05-01                 Midlands     64
## 301  2020-05-02                 Midlands     51
## 302  2020-05-03                 Midlands     52
## 303  2020-05-04                 Midlands     61
## 304  2020-05-05                 Midlands     59
## 305  2020-05-06                 Midlands     59
## 306  2020-05-07                 Midlands     48
## 307  2020-05-08                 Midlands     34
## 308  2020-05-09                 Midlands     37
## 309  2020-05-10                 Midlands     42
## 310  2020-05-11                 Midlands     33
## 311  2020-05-12                 Midlands     45
## 312  2020-05-13                 Midlands     40
## 313  2020-05-14                 Midlands     37
## 314  2020-05-15                 Midlands     40
## 315  2020-05-16                 Midlands     34
## 316  2020-05-17                 Midlands     31
## 317  2020-05-18                 Midlands     34
## 318  2020-05-19                 Midlands     34
## 319  2020-05-20                 Midlands     36
## 320  2020-05-21                 Midlands     32
## 321  2020-05-22                 Midlands     27
## 322  2020-05-23                 Midlands     34
## 323  2020-05-24                 Midlands     19
## 324  2020-05-25                 Midlands     26
## 325  2020-05-26                 Midlands     33
## 326  2020-05-27                 Midlands     29
## 327  2020-05-28                 Midlands     28
## 328  2020-05-29                 Midlands     20
## 329  2020-05-30                 Midlands     20
## 330  2020-05-31                 Midlands     22
## 331  2020-06-01                 Midlands     20
## 332  2020-06-02                 Midlands     22
## 333  2020-06-03                 Midlands     24
## 334  2020-06-04                 Midlands     16
## 335  2020-06-05                 Midlands     21
## 336  2020-06-06                 Midlands     20
## 337  2020-06-07                 Midlands     17
## 338  2020-06-08                 Midlands     16
## 339  2020-06-09                 Midlands     18
## 340  2020-06-10                 Midlands     15
## 341  2020-06-11                 Midlands     13
## 342  2020-06-12                 Midlands     12
## 343  2020-06-13                 Midlands      6
## 344  2020-06-14                 Midlands     17
## 345  2020-06-15                 Midlands     12
## 346  2020-06-16                 Midlands     14
## 347  2020-06-17                 Midlands     10
## 348  2020-06-18                 Midlands     14
## 349  2020-06-19                 Midlands      9
## 350  2020-06-20                 Midlands     13
## 351  2020-06-21                 Midlands     12
## 352  2020-06-22                 Midlands     12
## 353  2020-06-23                 Midlands     14
## 354  2020-06-24                 Midlands     13
## 355  2020-06-25                 Midlands     14
## 356  2020-06-26                 Midlands      3
## 357  2020-06-27                 Midlands      0
## 358  2020-03-01 North East and Yorkshire      0
## 359  2020-03-02 North East and Yorkshire      0
## 360  2020-03-03 North East and Yorkshire      0
## 361  2020-03-04 North East and Yorkshire      0
## 362  2020-03-05 North East and Yorkshire      0
## 363  2020-03-06 North East and Yorkshire      0
## 364  2020-03-07 North East and Yorkshire      0
## 365  2020-03-08 North East and Yorkshire      0
## 366  2020-03-09 North East and Yorkshire      0
## 367  2020-03-10 North East and Yorkshire      0
## 368  2020-03-11 North East and Yorkshire      0
## 369  2020-03-12 North East and Yorkshire      0
## 370  2020-03-13 North East and Yorkshire      0
## 371  2020-03-14 North East and Yorkshire      0
## 372  2020-03-15 North East and Yorkshire      2
## 373  2020-03-16 North East and Yorkshire      3
## 374  2020-03-17 North East and Yorkshire      1
## 375  2020-03-18 North East and Yorkshire      2
## 376  2020-03-19 North East and Yorkshire      6
## 377  2020-03-20 North East and Yorkshire      5
## 378  2020-03-21 North East and Yorkshire      6
## 379  2020-03-22 North East and Yorkshire      7
## 380  2020-03-23 North East and Yorkshire      9
## 381  2020-03-24 North East and Yorkshire      8
## 382  2020-03-25 North East and Yorkshire     18
## 383  2020-03-26 North East and Yorkshire     21
## 384  2020-03-27 North East and Yorkshire     28
## 385  2020-03-28 North East and Yorkshire     35
## 386  2020-03-29 North East and Yorkshire     38
## 387  2020-03-30 North East and Yorkshire     64
## 388  2020-03-31 North East and Yorkshire     60
## 389  2020-04-01 North East and Yorkshire     67
## 390  2020-04-02 North East and Yorkshire     74
## 391  2020-04-03 North East and Yorkshire    100
## 392  2020-04-04 North East and Yorkshire    105
## 393  2020-04-05 North East and Yorkshire     92
## 394  2020-04-06 North East and Yorkshire     96
## 395  2020-04-07 North East and Yorkshire    102
## 396  2020-04-08 North East and Yorkshire    107
## 397  2020-04-09 North East and Yorkshire    111
## 398  2020-04-10 North East and Yorkshire    117
## 399  2020-04-11 North East and Yorkshire     98
## 400  2020-04-12 North East and Yorkshire     84
## 401  2020-04-13 North East and Yorkshire     94
## 402  2020-04-14 North East and Yorkshire    107
## 403  2020-04-15 North East and Yorkshire     96
## 404  2020-04-16 North East and Yorkshire    103
## 405  2020-04-17 North East and Yorkshire     88
## 406  2020-04-18 North East and Yorkshire     95
## 407  2020-04-19 North East and Yorkshire     88
## 408  2020-04-20 North East and Yorkshire    100
## 409  2020-04-21 North East and Yorkshire     76
## 410  2020-04-22 North East and Yorkshire     84
## 411  2020-04-23 North East and Yorkshire     63
## 412  2020-04-24 North East and Yorkshire     72
## 413  2020-04-25 North East and Yorkshire     69
## 414  2020-04-26 North East and Yorkshire     65
## 415  2020-04-27 North East and Yorkshire     65
## 416  2020-04-28 North East and Yorkshire     57
## 417  2020-04-29 North East and Yorkshire     69
## 418  2020-04-30 North East and Yorkshire     57
## 419  2020-05-01 North East and Yorkshire     64
## 420  2020-05-02 North East and Yorkshire     48
## 421  2020-05-03 North East and Yorkshire     40
## 422  2020-05-04 North East and Yorkshire     49
## 423  2020-05-05 North East and Yorkshire     40
## 424  2020-05-06 North East and Yorkshire     51
## 425  2020-05-07 North East and Yorkshire     45
## 426  2020-05-08 North East and Yorkshire     42
## 427  2020-05-09 North East and Yorkshire     44
## 428  2020-05-10 North East and Yorkshire     40
## 429  2020-05-11 North East and Yorkshire     29
## 430  2020-05-12 North East and Yorkshire     27
## 431  2020-05-13 North East and Yorkshire     28
## 432  2020-05-14 North East and Yorkshire     31
## 433  2020-05-15 North East and Yorkshire     32
## 434  2020-05-16 North East and Yorkshire     35
## 435  2020-05-17 North East and Yorkshire     26
## 436  2020-05-18 North East and Yorkshire     30
## 437  2020-05-19 North East and Yorkshire     27
## 438  2020-05-20 North East and Yorkshire     22
## 439  2020-05-21 North East and Yorkshire     33
## 440  2020-05-22 North East and Yorkshire     22
## 441  2020-05-23 North East and Yorkshire     18
## 442  2020-05-24 North East and Yorkshire     26
## 443  2020-05-25 North East and Yorkshire     21
## 444  2020-05-26 North East and Yorkshire     21
## 445  2020-05-27 North East and Yorkshire     22
## 446  2020-05-28 North East and Yorkshire     21
## 447  2020-05-29 North East and Yorkshire     25
## 448  2020-05-30 North East and Yorkshire     20
## 449  2020-05-31 North East and Yorkshire     20
## 450  2020-06-01 North East and Yorkshire     17
## 451  2020-06-02 North East and Yorkshire     23
## 452  2020-06-03 North East and Yorkshire     23
## 453  2020-06-04 North East and Yorkshire     17
## 454  2020-06-05 North East and Yorkshire     18
## 455  2020-06-06 North East and Yorkshire     21
## 456  2020-06-07 North East and Yorkshire     14
## 457  2020-06-08 North East and Yorkshire     11
## 458  2020-06-09 North East and Yorkshire     12
## 459  2020-06-10 North East and Yorkshire     18
## 460  2020-06-11 North East and Yorkshire      7
## 461  2020-06-12 North East and Yorkshire      9
## 462  2020-06-13 North East and Yorkshire     10
## 463  2020-06-14 North East and Yorkshire     11
## 464  2020-06-15 North East and Yorkshire      9
## 465  2020-06-16 North East and Yorkshire     10
## 466  2020-06-17 North East and Yorkshire      9
## 467  2020-06-18 North East and Yorkshire     10
## 468  2020-06-19 North East and Yorkshire      6
## 469  2020-06-20 North East and Yorkshire      4
## 470  2020-06-21 North East and Yorkshire      4
## 471  2020-06-22 North East and Yorkshire      6
## 472  2020-06-23 North East and Yorkshire      7
## 473  2020-06-24 North East and Yorkshire      8
## 474  2020-06-25 North East and Yorkshire      3
## 475  2020-06-26 North East and Yorkshire      5
## 476  2020-06-27 North East and Yorkshire      0
## 477  2020-03-01               North West      0
## 478  2020-03-02               North West      0
## 479  2020-03-03               North West      0
## 480  2020-03-04               North West      0
## 481  2020-03-05               North West      1
## 482  2020-03-06               North West      0
## 483  2020-03-07               North West      0
## 484  2020-03-08               North West      1
## 485  2020-03-09               North West      0
## 486  2020-03-10               North West      0
## 487  2020-03-11               North West      0
## 488  2020-03-12               North West      2
## 489  2020-03-13               North West      3
## 490  2020-03-14               North West      1
## 491  2020-03-15               North West      4
## 492  2020-03-16               North West      2
## 493  2020-03-17               North West      4
## 494  2020-03-18               North West      6
## 495  2020-03-19               North West      7
## 496  2020-03-20               North West     10
## 497  2020-03-21               North West     11
## 498  2020-03-22               North West     13
## 499  2020-03-23               North West     15
## 500  2020-03-24               North West     21
## 501  2020-03-25               North West     21
## 502  2020-03-26               North West     29
## 503  2020-03-27               North West     35
## 504  2020-03-28               North West     28
## 505  2020-03-29               North West     46
## 506  2020-03-30               North West     67
## 507  2020-03-31               North West     52
## 508  2020-04-01               North West     86
## 509  2020-04-02               North West     96
## 510  2020-04-03               North West     95
## 511  2020-04-04               North West     98
## 512  2020-04-05               North West    102
## 513  2020-04-06               North West    100
## 514  2020-04-07               North West    135
## 515  2020-04-08               North West    127
## 516  2020-04-09               North West    119
## 517  2020-04-10               North West    117
## 518  2020-04-11               North West    138
## 519  2020-04-12               North West    125
## 520  2020-04-13               North West    129
## 521  2020-04-14               North West    131
## 522  2020-04-15               North West    114
## 523  2020-04-16               North West    135
## 524  2020-04-17               North West     98
## 525  2020-04-18               North West    113
## 526  2020-04-19               North West     71
## 527  2020-04-20               North West     83
## 528  2020-04-21               North West     76
## 529  2020-04-22               North West     86
## 530  2020-04-23               North West     85
## 531  2020-04-24               North West     66
## 532  2020-04-25               North West     65
## 533  2020-04-26               North West     55
## 534  2020-04-27               North West     54
## 535  2020-04-28               North West     57
## 536  2020-04-29               North West     62
## 537  2020-04-30               North West     59
## 538  2020-05-01               North West     45
## 539  2020-05-02               North West     56
## 540  2020-05-03               North West     55
## 541  2020-05-04               North West     48
## 542  2020-05-05               North West     48
## 543  2020-05-06               North West     44
## 544  2020-05-07               North West     49
## 545  2020-05-08               North West     42
## 546  2020-05-09               North West     30
## 547  2020-05-10               North West     41
## 548  2020-05-11               North West     35
## 549  2020-05-12               North West     38
## 550  2020-05-13               North West     25
## 551  2020-05-14               North West     26
## 552  2020-05-15               North West     33
## 553  2020-05-16               North West     32
## 554  2020-05-17               North West     24
## 555  2020-05-18               North West     31
## 556  2020-05-19               North West     35
## 557  2020-05-20               North West     27
## 558  2020-05-21               North West     27
## 559  2020-05-22               North West     26
## 560  2020-05-23               North West     31
## 561  2020-05-24               North West     26
## 562  2020-05-25               North West     31
## 563  2020-05-26               North West     27
## 564  2020-05-27               North West     27
## 565  2020-05-28               North West     28
## 566  2020-05-29               North West     20
## 567  2020-05-30               North West     19
## 568  2020-05-31               North West     13
## 569  2020-06-01               North West     12
## 570  2020-06-02               North West     27
## 571  2020-06-03               North West     22
## 572  2020-06-04               North West     22
## 573  2020-06-05               North West     16
## 574  2020-06-06               North West     26
## 575  2020-06-07               North West     20
## 576  2020-06-08               North West     20
## 577  2020-06-09               North West     16
## 578  2020-06-10               North West     16
## 579  2020-06-11               North West     16
## 580  2020-06-12               North West     11
## 581  2020-06-13               North West      9
## 582  2020-06-14               North West     15
## 583  2020-06-15               North West     15
## 584  2020-06-16               North West     13
## 585  2020-06-17               North West     10
## 586  2020-06-18               North West     13
## 587  2020-06-19               North West      7
## 588  2020-06-20               North West     11
## 589  2020-06-21               North West      6
## 590  2020-06-22               North West     10
## 591  2020-06-23               North West     13
## 592  2020-06-24               North West     13
## 593  2020-06-25               North West     11
## 594  2020-06-26               North West      2
## 595  2020-06-27               North West      1
## 596  2020-03-01               South East      0
## 597  2020-03-02               South East      0
## 598  2020-03-03               South East      1
## 599  2020-03-04               South East      0
## 600  2020-03-05               South East      1
## 601  2020-03-06               South East      0
## 602  2020-03-07               South East      0
## 603  2020-03-08               South East      1
## 604  2020-03-09               South East      1
## 605  2020-03-10               South East      1
## 606  2020-03-11               South East      1
## 607  2020-03-12               South East      0
## 608  2020-03-13               South East      1
## 609  2020-03-14               South East      1
## 610  2020-03-15               South East      5
## 611  2020-03-16               South East      8
## 612  2020-03-17               South East      7
## 613  2020-03-18               South East     10
## 614  2020-03-19               South East      9
## 615  2020-03-20               South East     13
## 616  2020-03-21               South East      7
## 617  2020-03-22               South East     25
## 618  2020-03-23               South East     20
## 619  2020-03-24               South East     22
## 620  2020-03-25               South East     29
## 621  2020-03-26               South East     35
## 622  2020-03-27               South East     34
## 623  2020-03-28               South East     36
## 624  2020-03-29               South East     55
## 625  2020-03-30               South East     58
## 626  2020-03-31               South East     65
## 627  2020-04-01               South East     66
## 628  2020-04-02               South East     55
## 629  2020-04-03               South East     72
## 630  2020-04-04               South East     80
## 631  2020-04-05               South East     82
## 632  2020-04-06               South East     88
## 633  2020-04-07               South East    100
## 634  2020-04-08               South East     83
## 635  2020-04-09               South East    104
## 636  2020-04-10               South East     88
## 637  2020-04-11               South East     88
## 638  2020-04-12               South East     88
## 639  2020-04-13               South East     84
## 640  2020-04-14               South East     65
## 641  2020-04-15               South East     72
## 642  2020-04-16               South East     56
## 643  2020-04-17               South East     86
## 644  2020-04-18               South East     57
## 645  2020-04-19               South East     70
## 646  2020-04-20               South East     87
## 647  2020-04-21               South East     51
## 648  2020-04-22               South East     54
## 649  2020-04-23               South East     57
## 650  2020-04-24               South East     64
## 651  2020-04-25               South East     51
## 652  2020-04-26               South East     51
## 653  2020-04-27               South East     40
## 654  2020-04-28               South East     40
## 655  2020-04-29               South East     47
## 656  2020-04-30               South East     29
## 657  2020-05-01               South East     37
## 658  2020-05-02               South East     36
## 659  2020-05-03               South East     17
## 660  2020-05-04               South East     35
## 661  2020-05-05               South East     29
## 662  2020-05-06               South East     25
## 663  2020-05-07               South East     27
## 664  2020-05-08               South East     26
## 665  2020-05-09               South East     28
## 666  2020-05-10               South East     19
## 667  2020-05-11               South East     25
## 668  2020-05-12               South East     27
## 669  2020-05-13               South East     18
## 670  2020-05-14               South East     32
## 671  2020-05-15               South East     24
## 672  2020-05-16               South East     22
## 673  2020-05-17               South East     18
## 674  2020-05-18               South East     22
## 675  2020-05-19               South East     12
## 676  2020-05-20               South East     22
## 677  2020-05-21               South East     15
## 678  2020-05-22               South East     17
## 679  2020-05-23               South East     21
## 680  2020-05-24               South East     17
## 681  2020-05-25               South East     13
## 682  2020-05-26               South East     19
## 683  2020-05-27               South East     18
## 684  2020-05-28               South East     12
## 685  2020-05-29               South East     21
## 686  2020-05-30               South East      8
## 687  2020-05-31               South East     12
## 688  2020-06-01               South East     11
## 689  2020-06-02               South East     13
## 690  2020-06-03               South East     17
## 691  2020-06-04               South East     11
## 692  2020-06-05               South East     11
## 693  2020-06-06               South East     10
## 694  2020-06-07               South East     12
## 695  2020-06-08               South East      8
## 696  2020-06-09               South East     10
## 697  2020-06-10               South East     11
## 698  2020-06-11               South East      5
## 699  2020-06-12               South East      6
## 700  2020-06-13               South East      6
## 701  2020-06-14               South East      7
## 702  2020-06-15               South East      7
## 703  2020-06-16               South East     11
## 704  2020-06-17               South East      8
## 705  2020-06-18               South East      4
## 706  2020-06-19               South East      6
## 707  2020-06-20               South East      5
## 708  2020-06-21               South East      3
## 709  2020-06-22               South East      2
## 710  2020-06-23               South East      8
## 711  2020-06-24               South East      6
## 712  2020-06-25               South East      4
## 713  2020-06-26               South East      3
## 714  2020-06-27               South East      2
## 715  2020-03-01               South West      0
## 716  2020-03-02               South West      0
## 717  2020-03-03               South West      0
## 718  2020-03-04               South West      0
## 719  2020-03-05               South West      0
## 720  2020-03-06               South West      0
## 721  2020-03-07               South West      0
## 722  2020-03-08               South West      0
## 723  2020-03-09               South West      0
## 724  2020-03-10               South West      0
## 725  2020-03-11               South West      1
## 726  2020-03-12               South West      0
## 727  2020-03-13               South West      0
## 728  2020-03-14               South West      1
## 729  2020-03-15               South West      0
## 730  2020-03-16               South West      0
## 731  2020-03-17               South West      2
## 732  2020-03-18               South West      2
## 733  2020-03-19               South West      4
## 734  2020-03-20               South West      3
## 735  2020-03-21               South West      6
## 736  2020-03-22               South West      7
## 737  2020-03-23               South West      8
## 738  2020-03-24               South West      7
## 739  2020-03-25               South West      9
## 740  2020-03-26               South West     11
## 741  2020-03-27               South West     13
## 742  2020-03-28               South West     21
## 743  2020-03-29               South West     18
## 744  2020-03-30               South West     23
## 745  2020-03-31               South West     23
## 746  2020-04-01               South West     22
## 747  2020-04-02               South West     23
## 748  2020-04-03               South West     30
## 749  2020-04-04               South West     42
## 750  2020-04-05               South West     32
## 751  2020-04-06               South West     34
## 752  2020-04-07               South West     39
## 753  2020-04-08               South West     47
## 754  2020-04-09               South West     24
## 755  2020-04-10               South West     46
## 756  2020-04-11               South West     43
## 757  2020-04-12               South West     23
## 758  2020-04-13               South West     27
## 759  2020-04-14               South West     24
## 760  2020-04-15               South West     32
## 761  2020-04-16               South West     29
## 762  2020-04-17               South West     33
## 763  2020-04-18               South West     25
## 764  2020-04-19               South West     31
## 765  2020-04-20               South West     26
## 766  2020-04-21               South West     26
## 767  2020-04-22               South West     23
## 768  2020-04-23               South West     17
## 769  2020-04-24               South West     19
## 770  2020-04-25               South West     15
## 771  2020-04-26               South West     27
## 772  2020-04-27               South West     13
## 773  2020-04-28               South West     17
## 774  2020-04-29               South West     15
## 775  2020-04-30               South West     26
## 776  2020-05-01               South West      6
## 777  2020-05-02               South West      7
## 778  2020-05-03               South West     10
## 779  2020-05-04               South West     17
## 780  2020-05-05               South West     14
## 781  2020-05-06               South West     19
## 782  2020-05-07               South West     16
## 783  2020-05-08               South West      6
## 784  2020-05-09               South West     11
## 785  2020-05-10               South West      5
## 786  2020-05-11               South West      8
## 787  2020-05-12               South West      7
## 788  2020-05-13               South West      7
## 789  2020-05-14               South West      6
## 790  2020-05-15               South West      4
## 791  2020-05-16               South West      4
## 792  2020-05-17               South West      6
## 793  2020-05-18               South West      4
## 794  2020-05-19               South West      6
## 795  2020-05-20               South West      1
## 796  2020-05-21               South West      9
## 797  2020-05-22               South West      6
## 798  2020-05-23               South West      6
## 799  2020-05-24               South West      3
## 800  2020-05-25               South West      8
## 801  2020-05-26               South West     11
## 802  2020-05-27               South West      5
## 803  2020-05-28               South West     10
## 804  2020-05-29               South West      7
## 805  2020-05-30               South West      3
## 806  2020-05-31               South West      2
## 807  2020-06-01               South West      7
## 808  2020-06-02               South West      2
## 809  2020-06-03               South West      7
## 810  2020-06-04               South West      2
## 811  2020-06-05               South West      2
## 812  2020-06-06               South West      1
## 813  2020-06-07               South West      3
## 814  2020-06-08               South West      3
## 815  2020-06-09               South West      0
## 816  2020-06-10               South West      1
## 817  2020-06-11               South West      2
## 818  2020-06-12               South West      2
## 819  2020-06-13               South West      2
## 820  2020-06-14               South West      0
## 821  2020-06-15               South West      1
## 822  2020-06-16               South West      2
## 823  2020-06-17               South West      0
## 824  2020-06-18               South West      0
## 825  2020-06-19               South West      0
## 826  2020-06-20               South West      2
## 827  2020-06-21               South West      0
## 828  2020-06-22               South West      1
## 829  2020-06-23               South West      1
## 830  2020-06-24               South West      1
## 831  2020-06-25               South West      0
## 832  2020-06-26               South West      1
## 833  2020-06-27               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-06-28"

The completion date of the NHS Pathways data is Sunday 28 Jun 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -10.6150   -3.1282   -0.3629    3.6398    6.0423  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.835e+00  5.509e-02   87.77   <2e-16 ***
## note_lag    1.255e-05  5.625e-07   22.32   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 14.22788)
## 
##     Null deviance: 7548.82  on 57  degrees of freedom
## Residual deviance:  823.59  on 56  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  125.854275    1.000013
exp(confint(lag_mod))
##                  2.5 %     97.5 %
## (Intercept) 112.824973 140.022959
## note_lag      1.000011   1.000014

Rsq(lag_mod)
## [1] 0.8908981

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.5.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.5.0: Tue May 26 20:41:44 PDT 2020; root:xnu-6153.121.2~2/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                                   "Mac-1911.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          0.2                         
## year           2020                        
## month          06                          
## day            22                          
## svn rev        78730                       
## language       R                           
## version.string R version 4.0.2 (2020-06-22)
## nickname       Taking Off Again

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 4.0.2 (2020-06-22)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.1     ggpubr_0.4.0         lubridate_1.7.9     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.14             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.1.1       
## [10] projections_0.5.0    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.1      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.5          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.0          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.0          tibble_3.0.1         ggplot2_3.3.2       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] colorspace_1.4-1  selectr_0.4-2     ggsignif_0.6.0    ellipsis_0.3.1   
##  [5] rprojroot_1.3-2   snakecase_0.11.0  fs_1.4.1          rstudioapi_0.11  
##  [9] farver_2.0.3      fansi_0.4.1       splines_4.0.2     knitr_1.29       
## [13] jsonlite_1.7.0    broom_0.5.6       dbplyr_1.4.4      compiler_4.0.2   
## [17] httr_1.4.1        backports_1.1.8   assertthat_0.2.1  Matrix_1.2-18    
## [21] cli_2.0.2         htmltools_0.5.0   prettyunits_1.1.1 tools_4.0.2      
## [25] gtable_0.3.0      glue_1.4.1        Rcpp_1.0.4.6      carData_3.0-4    
## [29] cellranger_1.1.0  vctrs_0.3.1       nlme_3.1-148      matchmaker_0.1.1 
## [33] crosstalk_1.1.0.1 xfun_0.15         ps_1.3.3          openxlsx_4.1.5   
## [37] lifecycle_0.2.0   rstatix_0.6.0     MASS_7.3-51.6     scales_1.1.1     
## [41] hms_0.5.3         sodium_1.1        yaml_2.2.1        curl_4.3         
## [45] gridExtra_2.3     stringi_1.4.6     kyotil_2019.11-22 boot_1.3-25      
## [49] pkgbuild_1.0.8    zip_2.0.4         rlang_0.4.6       pkgconfig_2.0.3  
## [53] evaluate_0.14     lattice_0.20-41   labeling_0.3      htmlwidgets_1.5.1
## [57] cowplot_1.0.0     processx_3.4.2    tidyselect_1.1.0  plyr_1.8.6       
## [61] magrittr_1.5      R6_2.4.1          generics_0.0.2    DBI_1.1.0        
## [65] pillar_1.4.4      haven_2.3.1       foreign_0.8-80    withr_2.2.0      
## [69] mgcv_1.8-31       survival_3.1-12   abind_1.4-5       modelr_0.1.8     
## [73] crayon_1.3.4      car_3.0-8         utf8_1.1.4        rmarkdown_2.3    
## [77] viridis_0.5.1     grid_4.0.2        readxl_1.3.1      data.table_1.12.8
## [81] blob_1.2.1        callr_3.4.3       reprex_0.3.0      digest_0.6.25    
## [85] webshot_0.5.2     munsell_0.5.0     viridisLite_0.3.0